By 'lowered rate deduction', do you mean a lower rate in general? Or is this some other term that I don't understand?
The mortgage rate deduction is flawed in that it provides a bigger benefit to those who are more affluent and it encourages people to buy more home than they need, which has all sorts of other implications. It would be better to have a lower rate, but I have no idea how you put that genie back in the bottle. Phasing out the home mortgage deduction would be very difficult and it would damage a lot of households. I don't know how you could even do it from a realistic perspective.
My ancestors fought cave bears so I could make this post.